messages listlengths 2 2 | topic stringclasses 4
values | difficulty stringclasses 3
values |
|---|---|---|
[
{
"role": "user",
"content": "Create an educational manim animation explaining SVD. Show the original matrix, the factorization, and the progressive reconstruction by adding rank-1 terms. Include a bar chart of singular values."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_... | linear_algebra | hard |
[
{
"role": "user",
"content": "Create a manim animation of a 3-state Markov chain showing state transitions and the probability distribution evolving toward the stationary distribution over 8 iterations."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: PLAN:\n1. Setu... | probability_stats | easy |
[
{
"role": "user",
"content": "Create an educational manim animation explaining how neural networks learn. Show forward pass (blue flow), loss computation, and backward pass (red gradient flow) on a 3-4-2 fully connected network."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem... | ml_ai | medium |
[
{
"role": "user",
"content": "Create a manim animation showing Bayesian updating with a Beta(1,1) prior and 5 Bernoulli observations. Animate the posterior shifting after each observation."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: The user wants a manim anima... | probability_stats | medium |
[
{
"role": "user",
"content": "Write a manim Scene called SVDDecomposition that breaks down SVD into a sum of rank-1 matrices. Show each component, accumulate them into a partial reconstruction, and compare with the original."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_ana... | linear_algebra | medium |
[
{
"role": "user",
"content": "Create a manim animation showing Riemann sums converging to the true integral of f(x) = x^2 on [0, 2]. Start with dx=1, then refine through 0.5, 0.25, and 0.1, showing the error decreasing at each step."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [pro... | calculus | medium |
[
{
"role": "user",
"content": "Create an educational manim animation explaining Fourier series. Show how a sum of sine waves can approximate a square wave, with each added harmonic bringing the approximation closer to the target."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem... | calculus | medium |
[
{
"role": "user",
"content": "Create a manim animation showing Fourier series approximation of a square wave. Start with 1 harmonic, then add 2 more at each step (up to 9 harmonics), showing the curve converging to the square wave."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [prob... | calculus | hard |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing Fourier series convergence. Display the target square wave, then progressively add harmonics (1, 3, 5, 7, 9) and show the approximation improving. Mention the Gibbs phenomenon."
},
{
"role": "assistant",
"content": "<reasoning... | calculus | medium |
[
{
"role": "user",
"content": "Write a manim Scene called BayesianUpdate that demonstrates how a Beta prior gets updated by Bernoulli observations. Show the curve evolving and label the final posterior mode."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: What is th... | probability_stats | hard |
[
{
"role": "user",
"content": "Animate K-means clustering in manim. Initialize 30 random points and 3 centroids, then show 5 iterations of the assign-update cycle with centroids moving and points changing color to match their cluster."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [pr... | ml_ai | medium |
[
{
"role": "user",
"content": "Write a manim Scene called SVDDecomposition that breaks down SVD into a sum of rank-1 matrices. Show each component, accumulate them into a partial reconstruction, and compare with the original."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_ana... | linear_algebra | hard |
[
{
"role": "user",
"content": "Create a manim animation visualizing SVD decomposition. Show a matrix M = U S V^T being reconstructed as a sum of rank-1 matrices sigma_i u_i v_i^T, with each component added one at a time."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis... | linear_algebra | hard |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing Markov chain convergence. Show the state graph with labeled transition probabilities, and a bar chart of the state distribution evolving toward steady state."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_... | probability_stats | hard |
[
{
"role": "user",
"content": "Create a manim animation visualizing SVD decomposition. Show a matrix M = U S V^T being reconstructed as a sum of rank-1 matrices sigma_i u_i v_i^T, with each component added one at a time."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis... | linear_algebra | medium |
[
{
"role": "user",
"content": "Create a manim animation visualizing the attention mechanism. Show Q, K, V matrices, compute QK^T / sqrt(d_k), apply softmax row-wise with a heatmap, and multiply by V to get the output."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: ... | ml_ai | medium |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing backpropagation. Show a 3-4-2 network, animate forward activations flowing left to right, display the loss, then animate gradients flowing backward in red."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_an... | ml_ai | medium |
[
{
"role": "user",
"content": "Animate gradient descent on a quadratic loss in manim. I want to see: axes, the curve f(x)=x^2, a red dot moving downhill, yellow tangent lines at each step, orange gradient arrows, and a final convergence label."
},
{
"role": "assistant",
"content": "<reasoning>\nS... | ml_ai | medium |
[
{
"role": "user",
"content": "Create a manim animation showing Riemann sums converging to the true integral of f(x) = x^2 on [0, 2]. Start with dx=1, then refine through 0.5, 0.25, and 0.1, showing the error decreasing at each step."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [pro... | calculus | medium |
[
{
"role": "user",
"content": "Create a manim animation of K-means clustering on 30 random 2D points with 3 clusters. Show centroid initialization, then iterate: assign points, update centroids, move centroids. Run 5 iterations."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_... | ml_ai | hard |
[
{
"role": "user",
"content": "Write a manim Scene class called GradientDescentFull that visualizes 8 steps of gradient descent on x^2 with learning rate 0.15, showing tangent lines, gradient arrows, and tracking each iterate with labels."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1... | ml_ai | hard |
[
{
"role": "user",
"content": "Write a manim Scene called KMeansConvergence that demonstrates K-means clustering. Use 30 points, 3 centroids (marked as X-shapes), and animate 5 iterations with assignment lines and color-coded clusters."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [p... | ml_ai | medium |
[
{
"role": "user",
"content": "Create a manim animation of K-means clustering on 30 random 2D points with 3 clusters. Show centroid initialization, then iterate: assign points, update centroids, move centroids. Run 5 iterations."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_... | ml_ai | medium |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing Markov chain convergence. Show the state graph with labeled transition probabilities, and a bar chart of the state distribution evolving toward steady state."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_... | probability_stats | medium |
[
{
"role": "user",
"content": "Create an educational manim animation explaining transformer attention. Visualize each matrix operation with proper labels and use a color-coded heatmap for the softmax weights."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: The user ... | ml_ai | easy |
[
{
"role": "user",
"content": "Animate Bayesian updating in manim. Use a Beta(1,1) prior and update with observations [H, H, T, H, H]. Show the posterior curve shifting and sharpening with each new data point."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: What is ... | probability_stats | easy |
[
{
"role": "user",
"content": "Animate the attention mechanism in manim. Show each step: QK^T, scaling by 1/sqrt(d_k), softmax row-wise (as a color heatmap), and the final matrix multiplication with V."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: Goal: animate Q,... | ml_ai | easy |
[
{
"role": "user",
"content": "Animate Fourier series approximation in manim. Use the standard square wave Fourier series, and visualize how adding more harmonics improves the approximation."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: The user wants a manim anim... | calculus | easy |
[
{
"role": "user",
"content": "Build a complex manim Scene visualizing the limit definition of the integral. Show Riemann sums with progressively smaller dx, alongside a bar chart of the approximation error converging to zero."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_an... | calculus | hard |
[
{
"role": "user",
"content": "Create a manim animation visualizing the attention mechanism. Show Q, K, V matrices, compute QK^T / sqrt(d_k), apply softmax row-wise with a heatmap, and multiply by V to get the output."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: ... | ml_ai | hard |
[
{
"role": "user",
"content": "Animate Bayesian updating in manim. Use a Beta(1,1) prior and update with observations [H, H, T, H, H]. Show the posterior curve shifting and sharpening with each new data point."
},
{
"role": "assistant",
"content": "<reasoning>\nStep 1 [problem_analysis]: What is ... | probability_stats | easy |
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